Devices and methods for providing stimulated raman lasing

ABSTRACT

Devices and methods for providing stimulated Raman lasing are provided. In some embodiments, devices include a photonic crystal that includes a layer of silicon having a lattice of holes and a linear defect that forms a waveguide configured to receive pump light and output Stokes light through Raman scattering, wherein the thickness of the layer of silicon, the spacing of the lattice of holes, and the size of the holes are dimensioned to provide Raman lasing. In some embodiments, methods include forming a layer of silicon, and etching the layer of silicon to form a lattice of holes with a linear defect that forms a waveguide configured to receive pump light and output Stokes light through Raman scattering, wherein the thickness of the layer of silicon, the spacing of the lattice of holes, and the size of the holes are dimensioned to provide Raman lasing.

FIELD OF THE INVENTION

This invention relates to Raman microlasers using photonic crystalwaveguides made from silicon to achieve Raman lasing.

BACKGROUND OF THE INVENTION

Stimulated Raman scattering (SRS) has a rich and evolving history sincethe development of the laser. In 1962, Woodbury and Ng discovered theSRS effect at infrared frequencies. [E. J. Woodbury and W. K. Ng, Proc.IRE 50, 2347 (1962)] Hellwarth quickly described this observation as atwo-photon process with a full quantum mechanical calculation. [R. W.Hellwarth, Theory of Stimulated Raman Scattering, Phys. Rev. 130, 1850(1963)] To account for anti-Stokes generation and higher-order Ramaneffects, however, Garmire et al. and Bloembergen and Shen then adoptedthe coupled-wave formalism to describe the stimulated Raman effect. [E.Garmire, E. Pandarese, and C. H. Townes, Coherently Driven MolecularVibrations and Light Modulation, Phys. Rev. Lett. 11, 160 (1963); N.Bloembergen and Y. R. Shen, Coupling Between Vibrations and Light Wavesin Raman Laser Media, Phys. Rev. Lett. 12, 504 (1964); Y. R. Shen and N.Bloembergen, Theory of Stimulated Brillouin and Raman Scattering, Phys.Rev. 137, A1787 (1965)] These understandings were later improved by theinclusion of self-focusing to account for the much larger gain observedin SRS.

Recent developments include coupling a high Q (“Q” is a quality factor)silica microsphere to an optical fiber to achieve a minimum threshold of62 μW, an example of which is illustrated in FIG. 1A. [S. M. Spillane,T. J. Kippenberg, and K. J. Vahala, Ultralow-threshold Raman laser usinga spherical dielectric microcavity, Nature 415, 621 (2002)] Higher-orderRaman modes were observed in addition to other nonlinearities such asfour-wave mixing and stimulated Brillouin scattering.

In a different line of researches that does not use SRS, variousresearches have demonstrated that a laser-reflowed silicon oxidemicroresonator with additional Er³⁺ doping can achieve low-thresholdlasing. [A. Polman, B. Min, J. Kalkman, T. J. Kippenberg, and K. J.Vahala, Ultralow-threshold erbium-implanted toroidal microlaser onsilicon, App. Phys. Lett. 84 (7), 1037, 2004)] Concurrently, Claps etal. have demonstrated a small but first-ever Raman amplification insilicon on-chip waveguides for photonic integrated circuit applications.[R. Claps, D. Dimitropoulos, V. Raghunathan, Y. Han, and B. Jalali,Observation of stimulated Raman amplification in silicon waveguides,Optics Express 11 (15), 0.1731 (2003)] FIG. 1B illustrates an example ofsuch a waveguide that is a centimeter long.

However, presently, the development of sizable gain in silicon photonicintegrated circuits has yet to be demonstrated. This is suspected due toun-optimized phase matching design of the optical structures. [R. H.Stolen and E. P. Ippen, Raman gain in glass optical waveguides, App.Phys. Lett. 22 (6), 276 (1973)]

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the present invention will be best understood when readin reference to the accompanying figures wherein:

FIG. 1A is a magnified view of a conventional microsphere made fromsilica;

FIG. 1B is a magnified view of a conventional waveguide having its modalarea of approximately 2-4 μm² and the length of approximately 10,000 μm;

FIG. 2 is a magnified view of an example photonic crystal with awaveguide manufactured in accordance with various embodiments of thepresent invention;

FIG. 3 is a graphical illustration of a relationship between pump light,Stokes light, and phonons in Raman scattering for various embodiments ofthe present invention;

FIGS. 4 and 5 are graphical illustrations of a calculated band structuredepicting possible guided modes for various embodiments of the presentinvention;

FIGS. 4A and 5A are magnified views of portions of FIG. 4 and FIG. 5,respectively;

FIG. 6 is illustrations of electric and magnetic field intensitydistributions for various embodiments of the present invention;

FIGS. 7( a)-(c) are SEM pictures of an example slow-light PhC waveguidefabricated in accordance with various embodiments of the presentinvention;

FIG. 8 are pictures showing an example fiber coupling setup inaccordance with various embodiments of the present invention;

FIG. 9 is a graphical illustration of transition spectrum of an exampleof PhC waveguide fabricated in accordance with various embodiments ofthe present invention; and

FIG. 10 is a block diagram illustrating various components for usingpulsed pump light in various embodiments of the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE PRESENT INVENTION

SRS is a linear inelastic two-photon process, where an incident photoninteracts with an excited state of the material. In various embodimentsof the present invention, which include the use of photonic crystalsmade of silicon, the excited state of the material refers to thelongitudinal optical (LO) and transversal optical (TO) phonons ofcrystal silicon. In such embodiments, the strongest Stokes peak arisesfrom single first-order Raman-phonon (threefold degenerate) at theBrillouin zone center of silicon. A microscopic description that depictsthe change in the average number of photons n_(s) at the Stokeswavelength ω_(s) with respect to the longitudinal distance z is:

$\begin{matrix}{{\frac{n_{s}}{z} = {\left( {G_{R} \cdot \alpha_{s}} \right)n_{s}}},{G_{R} = {\frac{W_{fi}}{\omega_{s}}\left( {\rho_{i} \cdot \rho_{f}} \right)\frac{1}{\mu^{1/2}n_{s}}}},} & (1)\end{matrix}$

where G_(R) is the Raman gain, α_(s) an attenuation coefficient, μ thepermeability,

$\frac{W_{fi}}{\omega_{s}}$

the transition rate, and ρ_(i) and ρ_(f) the initial and final statepopulations, respectively. For n_(s) and n_(p) (the average number ofphotons at ω_(p)) significantly greater than 1,

$\frac{W_{fi}}{\omega_{s}} \propto {n_{s}n_{p}}$

and thus the Raman gain G_(R) is ∝n_(p). For large n_(s) and n_(p), amesoscopic classical description with Maxwell equations using nonlinearpolarizations P⁽³⁾ can also be used. The wave equations describing theinteractions are:

$\begin{matrix}{{{\nabla{\times \left( {\nabla{\times E_{s}}} \right)}} + {\frac{1}{c^{2}}\frac{\partial^{2}}{\partial t^{2}}\left( {ɛ_{s}E_{s}} \right)}} = {{- \frac{1}{c^{2}}}\frac{\partial^{2}}{\partial t^{2}}\left( P_{s}^{(3)} \right)}} & (2) \\{{{\nabla{\times \left( {\nabla{\times E_{p}}} \right)}} + {\frac{1}{c^{2}}\frac{\partial^{2}}{\partial t^{2}}\left( {ɛ_{p}E_{p}} \right)}} = {{- \frac{1}{c^{2}}}\frac{\partial^{2}}{\partial t^{2}}{\left( P_{p}^{(3)} \right).}}} & (3)\end{matrix}$

Specifically,

${P_{s}^{(3)} = {\chi^{\overset{(3)}{jkmn}}E_{p}E_{p}^{*}E_{s}}},$

where

$\chi^{\overset{(3)}{jkmn}}$

is the third-order fourth-rank Raman susceptibility with{j,k,m,n}={x,y,z}. The resonant terms in P_(s) ⁽³⁾ give rise to SRS,while the non-resonant terms add to self-focusing and field-inducedbirefringence. The E_(p) and E_(s) are the electric fields at the pumpand Stokes wavelengths, respectively. With

$\chi^{\overset{(3)}{jkmn}}$

obtained from bulk material properties, Equations (2) and (3) can beturned into discrete forms in the time-domain for direct ab initionumerical calculations of the nonlinear response.

As an approximation to the direct solution of this wave interpretation,the coupled-mode theory can be used to estimate the stimulated Ramangain. In particular, under the assumption of weak coupling between thepump and Stokes waves, the mode amplitudes can be given as:

$\begin{matrix}{\frac{\partial E_{p}}{\partial\underset{\_}{z}} = {{- }\; \beta_{pp}I_{p}E_{p}}} & (4) \\{\frac{\partial E_{s}}{\partial\underset{\_}{z}} = {{{- {\left( {{\beta_{p\; s}\left( \omega_{s} \right)} + {\kappa_{p\; s}\left( \omega_{s} \right)}} \right)}}I_{p}E_{s}} - {{\left( {{\beta_{p\; a}\left( \omega_{s} \right)} + {\kappa_{p\; a}\left( \omega_{s} \right)}} \right)}E_{p}^{2}E_{a}^{*}^{{- }\; \Delta \; {kz}}}}} & (5) \\{\frac{\partial E_{a}}{\partial\underset{\_}{z}} = {{{- {\left( {{\beta_{p\; a}\left( \omega_{a} \right)} + {\kappa_{p\; a}\left( \omega_{a} \right)}} \right)}}I_{p}E_{a}} - {{\left( {{\beta_{p\; s}\left( \omega_{a} \right)} + {\kappa_{p\; s}\left( \omega_{a} \right)}} \right)}E_{p}^{2}E_{s}^{*}^{{- }\; \Delta \; {kz}}}}} & (6)\end{matrix}$

where the self-coupling terms are neglected, E_(p), E_(s) and E_(a)denote the pump, and Stokes and anti-Stokes field amplitudes aredenoted, respectively, as I_(p)=|E_(p)|², I_(s)=|E_(p)|². β_(ab) denotesthe non-resonant terms and resonant terms with no frequency dependence.κ_(ab) denotes the resonant overall coupling coefficients (integratedspatially) between the modes. By determining κ_(ps)(ω_(s)), Equations(4) and (5) can be employed to determine the SRS gain. Intrinsic lossdue to two-photon absorption (TPA) is assumed to be small based on themeasured TPA coefficients in silicon and at pump powers on the order of1 W. The role of TPA-induced free carrier absorption is also reduced insub-wavelength silicon-on-insulator (SOI) waveguides of variousembodiments of the present invention due to significantly shorterlifetime (compared to the recombination lifetime). This results in loweroverall carrier densities.

Dimitropoulos et al. have derived a specialized form of Equations (5) todetermine the Raman gain G_(R) in waveguides. [D. Dimitropoulos, B.Houshmand, R. Claps, and B. Jalali, Coupled-mode theory of the Ramaneffect in silicon-on-insulator waveguides, Optics Lett. 28 (20), 1954(2003)] In particular, G_(R) has an approximate 1/(modal area)^(3/4)dependence; that is, the SRS gain increases with decreasing modal areas,such as from high-index contrast waveguide structures. In variousembodiments of the present invention, as will be described in detaillater, enhancements through smaller modal areas A_(m) and length scalesx, Purcell enhancements and/or slow group velocities afforded byphotonic crystal structures permit increased amplification withsignificantly smaller device length scales.

An example photonic crystal 201 manufactured in accordance with variousembodiments of the present invention is illustrated in FIG. 2. Inparticular, the photonic crystal 201 is formed from a layer of siliconon an insulator layer (e.g., a layer of oxide, SiO₂) (not shown). Thelayer of silicon can be formed by any known semiconductor fabricationmethod. For example, the layer of silicon can be deposited or grown onthe layer underneath it. In another example, a prefabricated wafer thathas a silicon layer already formed on an oxide layer can be used. Alattice of air-holes 203 is formed by etching the silicon layer.Although FIG. 2 illustrates the air-holes having a cylindrical shape,the air-holes can be in other shapes (e.g., rectangular, ellipsoidal,etc.) for some embodiments. The air-holes are not required to formperfect cylindrical shapes. The air-holes can have rough edges typicallyintroduced during fabrication processes. The depth of the air-holes canbe substantially equal to the thickness of the silicon layer (e.g., 300nm). However, the air-holes can be shallower or deeper than the siliconlayer. The etching of the silicon layer can be achieved by any knownmethod (e.g., plasma etching, wet etching, etc.).

The lattice of air-holes also forms basic patterns 205. The example inFIG. 2 illustrates the basic lattice as having a triangular shape.However, the lattice can be formed using other basic patterns (e.g.,squares, rectangles, pentagons, etc.). The etching step also createsdefects (e.g., areas with no air-holes) in the lattice. In FIG. 2, thedefects form a line of air-hole free region that is a pathway, which isan optical waveguide 207. Typically, a waveguide means opticallytransparent or low attenuation material that is used for thetransmission of signals with light waves. As used in connection withvarious embodiments of the present invention, a waveguide is alsocapable of lasing using Raman scattering.

The Raman scattering is further described using the example waveguide207 shown in FIG. 2. A light pump (not shown) coupled to the waveguide207 supplies a beam of light (hereinafter the pump light) to an inputport 209 of the waveguide 207. The pump light has a certain frequencyand a corresponding wavelength. As the pump light enters and travels toan output port 211 of the waveguide 207, the pump light is downshiftedto become Stokes light, as well as causing phonons to appear. Theproduction of Stokes light and phonons from the pump light is referredto as Raman scattering. The relationship between the pump light, Stokeslight, and phonons is graphically illustrated in FIG. 3.

FIG. 2 is a magnified view of an example photonic crystal. In fact,photonic crystals of various embodiments of the present invention havelengths on order of micrometers. For instance, the length can be between2-3 micrometers. In some embodiments, the length can be 2.5 micrometers.However, the length can be shorter or longer than these example rangesdepending on the overall design of each photonic crystal. Regarding thewaveguide 207, its length (i.e., the distance between the input port 209and output port 211) can be as co-extensive as that of the photoniccrystal 201. A rectangular cross-sectional area 213 of the waveguide 207perpendicular to the propagation direction of light in the waveguide 207(i.e., from the input port 209 to the output port 211) is preferably onorder of sub-wavelength. Such a cross-sectional area is also referred toas a model area. Here, sub-wavelength refers to lengths shorter than thewavelength of a light beam (either the pump light or the Stokes light),which is approximately 1.5 micrometers. In other words, each side of therectangular cross-section 213 of the waveguide 207 is shorter than thewavelength of a light beam. In some embodiments, the rectangularcross-sectional area is on order of sub-microns. This means each side ofthe rectangular cross-section of the waveguide is shorter than a micron.

The small cross-sectional area of the waveguide 207 causes optical fielddensities to increase and causes the gain of the Raman scattering andlasing to increase as well. In addition to this enhancement, variousembodiments of the present invention take advantage of slow lightphenomena. That is, at the photonic band edge, photons experiencemultiple reflections and move very slowly through the materialstructure. In photonic crystal structures, line-defects in the periodiclattice permit guided-mode bands within the band gap, as shown in FIGS.4 and 5. In various embodiments of the present invention, these bandsare designed to be as flat as possible (v_(g)≡dω/dk) to achieveslow-light behavior, shown in FIGS. 4A and 5A. Group velocities as lowas 10⁻² c can be obtained (“c” is the speed of light). Alternatively,coupled resonator optical waveguides can also permit control on thegroup velocity dispersion.

With slow group velocities, it is possible to reduce the interactionlength by (v_(g)/c)². In particular, for group velocities on order of10⁻² c, interaction lengths—between the Stokes and pump modes, forexample—on order of 10⁴ times smaller than conventional lasers can beobtained. For the same operation power, the same gain can be obtained bythe time-averaged Poynting power density P (˜v_(g)∈|E|²) incident on thephotonic crystal structure. A decrease in v_(g) leads to a correspondingincrease in ∈|E|² and in the Raman gain coefficient. These line-defectwaveguides can be designed for two modes (i.e., the pump and Stokesmodes) to be supported within the band gap of various embodiments of thepresent invention.

The small group velocity at the band edge in a 2D PhC lattice couldfurther be employed in photonic band edge lasers. Without requiring aresonant cavity, the photonic band edge is a 2D analog of thedistributed feedback laser. The lasing threshold is estimated to beproportional to v_(g) ² for operation at slow group velocity regions,arising from the enhanced stimulated emission and the increase in thereflection coefficient for small v_(g). This raises the possibility of aphotonic band edge Raman laser when optically pumped.

PhC Waveguide Modes Design

An example structure is an air-bridge triangular lattice photoniccrystal slab (e.g., 201) with thickness of 0.6a and the radius of airholes r is 0.29a, where a is the lattice period. The photonic band gapin this slab for TE-like modes is around 0.25˜0.32 [c/a] in frequency.The PhC waveguide is created by filling a row of air holes. FIG. 5 showsthe projected band diagram of a PhC waveguide calculated by MIT PhotonicBands (MPB) package. Two defect waveguide modes (0^(th) order and 1^(st)order) exist in the bandgap of the 2D PhC, and these waveguide modesshow high density states and zero group velocities at the band edge dueto the Bragg condition. The 1^(st) order and the 0^(th) order waveguidemodes at the band edge are considered to be pump mode and Stokes moderespectively. By tuning the geometry of PhC waveguide, such as the sizeof airholes, the waveguide width, and the slab thickness, thefrequencies of the two modes can be shifted to match the pump-Stokesfrequency spacing of 15.6 THz, corresponding to the optical phononfrequency of stimulated Raman scattering (SRS) in monolithic silicon.

The numerical design process is as following: (1) Fine-tune the PhCwaveguide geometry; (2) Calculate resonant frequencies f_(pump) andf_(Stokes) with MPB; (3) Calculate the lattice constant a based on thefrequencies (f_(pump)−f_(Stokes))(c/a)=15.6 Hz and calculate thewavelength=λ_(pump)=a/f_(pump), λ_(Stokes)=a/f_(Stakes). For example,when a=420 nm, (f_(pump)−f_(Stakes))=0.02184, with λ_(pump)=1550 nm,λ_(Stokes)=1686 nm. FIG. 2 shows the electric field intensity |E|² andthe magnetic field intensity |H|² at the middle of the slab for pumpmode (1^(st) order waveguide mode) and Stokes mode (0^(th) orderwaveguide mode) respectively.

Fabrication and Measurements

FIG. 7 shows the SEM pictures of PhC waveguide fabricated using asilicon-on-insulator (SOI) substrate with top silicon thickness of 320nm. The pump-Stokes frequency spacing can be obtained by active trimmingof PhC thickness. A potential issue for small v_(g) modes is theimpedance and mode mismatch when coupling into these waveguides. Inorder to decrease the coupling loss between the conventional ridgewaveguide and the PhC waveguide, the taper structure for adiabatic modetransformation is designed, as shown in FIG. 7 (c).

UWS-1000 Supercontinuum laser is used to provide a measurement windowfrom 1200 to 2000 nm. A polarization controller and a fiber-coupled lensassembly were used to couple light into the structure. A second lensedfiber collects the waveguide output that is sent to the optical spectrumanalyzer. The fiber coupling setup is shown in FIG. 8. The measuredtransmission spectrum of PhC waveguide is given in FIG. 9.

The amplification gain improved by the waveguides is further enhanced byintegrating a p-i-n (p-type, intrinsic, n-type) junction diode with thephotonic crystal. In such a configuration, the strong electrical fieldcreated by the diode removes free carriers (electrons and holes). Thesefree carriers, which are induced by two-photon absorption, can reduce,if not removed, the amplification gain factor in the photonic crystal.The p-i-n diode can be fabricated using any known semiconductorfabrication method. In operation, the diode is biased by a constantvoltage.

For various embodiments of the present invention, in order to provide anet Raman gain, TPA induced the free-carrier absorption phenomenon canalso be addressed using pulsed operations, where the carrier lifetime ismuch larger than the pulse width and much less than the pulse period. Inparticular, as shown in FIG. 10, a photonic crystal 1001 with one ormore microcavities is coupled to a multiplexer (MUX) 1003. The MUX 1003receives its input from a polarization controller 1005 that combinesinputs from a pulsed pump laser 1007 and a continuous wave (CW) Stokeslaser 1009. The output from the photonic crystal 1001 is then input toan optical spectrum analyzer (e.g., a detector) 1011.

Various embodiments of the present invention relate to methods ofmanufacturing a laser device. The methods may include the acts offorming a layer of silicon; and etching the silicon layer to form alattice of regularly spaced air-holes with a linear defect created by arow of missing air-holes. The linear defect forms a waveguide thatreceives pump light and outputs Stokes light through Raman scattering.The methods may further include acts of selecting frequencies of thepump light and the Stokes light from slow group velocity modes of thepump light and Stokes light in the waveguide. The slow group velocity isabout 1/100 of the speed of light. A distance between two regularlyspaced air-holes is approximately 420 nm.

Various embodiments of the present invention relate to devices forgenerating a laser beam. The devices may include a layer of photoniccrystal having a lattice of regularly spaced air-holes with a lineardefect created by a row of missing air-holes. The linear defect forms awaveguide that receives pump light and outputs Stokes light-throughRaman scattering. The frequencies of the pump light and the Stokes lightare selected from slow group velocity modes of the pump light and Stokeslight in the waveguide. The slow group velocity is about 1/100 of thespeed of light.

Various embodiments and advantages of the present invention are apparentfrom the detailed specification, and, thus, it is intended by theappended claims to cover all such features and advantages of theinvention which fall within the true spirit and scope of the invention.Further, since numerous modifications and variations will readily occurto those skilled in the art, it is not desired to limit the invention tothe exact construction and operation illustrated and described, and,accordingly, all suitable modifications and equivalents may be resortedto falling within the scope of the invention. The foregoing inventionhas been described in detail by way of illustration and example ofvarious embodiments, numerous modifications, substitutions, andalterations are possible without departing from the scope of theinvention.

1. A device for providing stimulated Raman lasing, comprising: aphotonic crystal that includes a layer of silicon having a lattice ofholes and a linear defect that forms a waveguide configured to receivepump light and output Stokes light through Raman scattering, wherein thethickness of the layer of silicon, the spacing of the lattice of holes,and the size of the holes are dimensioned to cause the photonic crystalto provide Raman lasing.
 2. The device of claim 1, wherein the thicknessof the layer of silicon is within a range of about 240 nm to about 265nm, the spacing of the holes is within a range of about 399 mm to about441 nm, and the size of the holes is within a range of about 166 nm toabout 122 nm.
 3. The device of claim 1, wherein the thickness of thelayer of silicon is within a range of about 216 nm to about 238 nm, thespacing of the holes is within a range of about 360 nm to about 400 nm,and the size of the holes is within a range of about 79 nm to about 87nm.
 4. The device of claim 1, wherein the waveguide is configured tocause the pump light to be in a slow group velocity mode.
 5. The deviceof claim 1, wherein the slow group velocity mode has a slow groupvelocity as low as about 1/1000 the speed of light.
 6. The device ofclaim 5, wherein the waveguide is configured to receive pump light witha wavelength of about 1550 nm.
 7. The device of claim 1, wherein theholes are regularly spaced and arranged in a repeating triangularpattern.
 8. The device of claim 1, further comprising forming anadiabatic coupling region between an input waveguide and the lattice ofholes forming a waveguide.
 9. The device of claim 1, further comprisinga p-i-n diode coupled to the waveguide that removes free carriers in thewaveguide.
 10. A method of manufacturing a photonic crystal waveguidefor providing stimulated Raman lasing, comprising: forming a layer ofsilicon; and etching the layer of silicon to form a lattice of holeswith a linear defect, such that the lattice of holes forms a waveguideconfigured to receive pump light and output Stokes light through Ramanscattering, wherein the thickness of the layer of silicon, the spacingof the lattice of holes, and the size of the holes are dimensioned tocause the photonic crystal to provide Raman lasing.
 11. The method ofclaim 10, wherein the thickness of the layer of silicon is within arange of about 240 nm to about 265 nm, the spacing of the holes iswithin a range of about 399 nm to about 441 nm, and the size of theholes is within a range of about 166 nm to about 122 nm.
 12. The deviceof claim 10, wherein the thickness of the layer of silicon is within arange of about 216 nm to about 238 nm, the spacing of the holes iswithin a range of about 360 nm to about 400 nm, and the size of theholes is within a range of about 79 nm to about 87 nm.
 13. The method ofclaim 10, wherein the waveguide is configured so that pump light of achosen frequency will be in a slow group velocity mode of the waveguide.14. The method of claim 10, wherein the slow group velocity mode has aslow group velocity as low as about 1/1000 the speed of light.
 15. Themethod of claim 14, wherein the wavelength of the selected frequency isabout 1550 nm
 16. The method of claim 10, further comprising etching thelattice of holes, such that a triangular pattern is formed.
 17. Themethod of claim 10, further comprising trimming the photonic crystalusing etching techniques.
 18. The method of claim 10, further comprisingforming an adiabatic coupling region between an input waveguide and thelattice of holes forming a waveguide.